1. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about centimeter across.
The length of these numbers in standard notation makes them awkward to work with.
Scientific notation is a shorthand way of writing such numbers.

2. Numbers written in scientific notation are written as two factors
Numbers written in scientific notation are written as two factors. One factor is a number greater than or equal to 1 and less than 10. The other factor is a power of 10.

3. Think: Move the decimal right 5 places. 135,000
Additional Example 1A: Translating Scientific Notation to Standard Notation
Write the number in standard notation.
1.35  105
1.35  10 5
10 = 100,000 5
1.35  100,000
Think: Move the decimal right 5 places.
135,000
A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.
Helpful Hint

4. Divide by the reciprocal.
Additional Example 1B: Translating Scientific Notation to Standard Notation Continued
Write the number in standard notation.
2.7  10–3
2.7  10–3
10 = –3 1
1000
2.7  1
1000
2.7 1000
Divide by the reciprocal.
0.0027
Think: Move the decimal left 3 places.

6. To write scientific notation for numbers greater than or equal to 1 and less than 10, use a 0 exponent = 5.63 x 10°.
Writing Math

7. Additional Example 2: Translating Standard Notation to Scientific Notation
Write in scientific notation.
Think: The decimal needs to move 3 places to get a number between 1 and 10.
7.09
7.09  10
Set up scientific notation.
Think: The decimal needs to move left to change to , so the exponent will be negative.
So written in scientific notation is 7.09  10–3.
Check  10–3 = 7.09  =